Background. The work examines the development and promotion of post-quantum standards, as well as the analysis and improvement of existing algorithms, on the basis of which the functioning of standards in the field of electronic digital signature can be based. One of the main reasons was also the migration of classical cryptography to post-quantum cryptography. The robot is aligning three popular post-quantum standards: CRYSTALS-Dilithium, Falcon and SPHINCS+. As a result of the investigation, the most optimal standards were selected before implementation of classical electronic signature schemes. The article is dedicated to the development and promotion of post-quantum standards in the field of electronic digital signature. It is also necessary to analyze and level up existing algorithms, on the basis of which the functioning of such standards can be based. The research is considered relevant due to the growing interest in quantum technologies and the need for secure electronic communications in the upcoming quantum world. Мethods. Мigrating classical cryptography to post-quantum cryptography. However, power is important, because the power of quantum computers can be affected by certain cryptographic algorithms. An analysis of the feasibility of transitioning to new standards and their existing security capabilities is also carried out. In addition, three popular post-quantum standards are being updated: CRYSTALS-Dilithium, Falcon and SPHINCS+. This allows us to determine the most optimal and reliable standard for implementation of classical electronic signature schemes. The authors of the work carry out the selection of the optimal standard, ensuring the safety and security of its authorities. Results. Сontains important results from the study of post-quantum standards for electronic digital signatures, which may be useful for developers of cryptographic software and information security engineers. The power supply to the influences and changes in the advanced post-quantum standards, such as the complexity of implementation, the flexibility of infrastructure and power standardization, are thoroughly examined. The prospects for the future development of post quantum cryptography and its influx into modern electronic signature systems have also been highlighted. This will help readers to take away the more common sense and context of the importance and potential contributions in this area. Conclusions. Falcon and CRYSTALS-Dilithium have a high signing fluidity and a larger key size, making them practical for rich stagnation. SPHINCS+, regardless of its viscosity, has less fluidity and requires a larger key size. The choice between CRYSTALS-Dilithium, Falcon and SPHINCS+ will depend on the specific drying needs, as well as compromises between fluidity, key size and viscosity. This demonstrates the high speed of subscription, and this is one of its key advantages. It is intended for use in quick operations, for example, on servers and industrial systems.
Background. The work examines the development and promotion of post-quantum standards, as well as the analysis and improvement of existing algorithms, on the basis of which the functioning of standards in the field of electronic digital signature can be based. One of the main reasons was also the migration of classical cryptography to post-quantum cryptography. The robot is aligning three popular post-quantum standards: CRYSTALS-Dilithium, Falcon and SPHINCS+. As a result of the investigation, the most optimal standards were selected before implementation of classical electronic signature schemes. The article is dedicated to the development and promotion of post-quantum standards in the field of electronic digital signature. It is also necessary to analyze and level up existing algorithms, on the basis of which the functioning of such standards can be based. The research is considered relevant due to the growing interest in quantum technologies and the need for secure electronic communications in the upcoming quantum world. Мethods. Мigrating classical cryptography to post-quantum cryptography. However, power is important, because the power of quantum computers can be affected by certain cryptographic algorithms. An analysis of the feasibility of transitioning to new standards and their existing security capabilities is also carried out. In addition, three popular post-quantum standards are being updated: CRYSTALS-Dilithium, Falcon and SPHINCS+. This allows us to determine the most optimal and reliable standard for implementation of classical electronic signature schemes. The authors of the work carry out the selection of the optimal standard, ensuring the safety and security of its authorities. Results. Сontains important results from the study of post-quantum standards for electronic digital signatures, which may be useful for developers of cryptographic software and information security engineers. The power supply to the influences and changes in the advanced post-quantum standards, such as the complexity of implementation, the flexibility of infrastructure and power standardization, are thoroughly examined. The prospects for the future development of post quantum cryptography and its influx into modern electronic signature systems have also been highlighted. This will help readers to take away the more common sense and context of the importance and potential contributions in this area. Conclusions. Falcon and CRYSTALS-Dilithium have a high signing fluidity and a larger key size, making them practical for rich stagnation. SPHINCS+, regardless of its viscosity, has less fluidity and requires a larger key size. The choice between CRYSTALS-Dilithium, Falcon and SPHINCS+ will depend on the specific drying needs, as well as compromises between fluidity, key size and viscosity. This demonstrates the high speed of subscription, and this is one of its key advantages. It is intended for use in quick operations, for example, on servers and industrial systems.
The continuous development of quantum computing requires the development of cryptographic algorithms resistant to quantum cryptanalysis. Therefore, the National Institute of Standards and Technology (NIST) is holding a competition to standardize algorithms in the post-quantum period, including Crystals-Dilithium, Falcon, and Sphincs+ for digital signatures. In order to determine the ways of development and ways to improve the existing methods of cryptographic protection and electronic digital signature (EDS), an urgent task arose to assess the effectiveness (stability and computational complexity) of existing EDS algorithms. In this paper, a comparative evaluation of EDS algorithms was carried out by key indicators. Research results show the disadvantages and advantages of each algorithm, taking into account the importance of context-specific use. The conclusions indicate that Dilithium has the lowest load on the system's computing resources, Falcon stands out for its signature verification speed, and Sphincs+ provides reliable security. The capabilities of existing cryptographic transformation algorithms based on elliptic curves do not meet the growing need of authentication algorithms resistance to quantum cryptanalysis, and the use of modern candidates for the post-quantum cryptography standard does not allow for a short-term transition to the usage of new cryptographic algorithms in information systems. The paper also points out the impossibility of simultaneous transition to potentially quantum cryptanalysis-resistant algorithms in existing information systems. The direction of further research is the development of new cryptoalgorithms and methods that will ensure the integrity and confidentiality of information during its transmission over unprotected channels in the transition period to the widespread use and implementation of post-quantum cryptography standards.
The National Institute of Standards and Technology (NIST) has recently concluded the third round of its Post Quantum Cryptography Standardization Process, selecting four finalist algorithms for standardization: CRYSTALS Kyber, CRYSTALS-Dilithium, FALCON, and SPHINCS+. These algorithms are designed to withstand attacks from both classical and quantum computers, ensuring the long-term security of digital communications. This paper presents a comprehensive comparative analysis of the security margins and practical deployment readiness of these finalist algorithms. CRYSTALS-Kyber, a key encapsulation mechanism based on the hardness of the Module Learning With Errors problem, offers strong security and efficient performance. CRYSTALS-Dilithium, a digital signature algorithm based on module lattices, provides robust security guarantees and relatively straightforward implementation. FALCON, a lattice-based digital signature algorithm utilizing the Fast Fourier Transform, offers compact signatures and fast verification but faces implementation challenges due to its reliance on floating-point arithmetic. SPHINCS+, a hash-based signature scheme, stands out as a conservative choice with security based solely on the well-established security of hash functions. The analysis reveals that while each algorithm has its strengths, they also face unique challenges in terms of side-channel vulnerabilities, formal security proofs, and performance trade-offs. The practical deployment of these algorithms requires careful consideration of specific security requirements, performance needs, and resource constraints. Ongoing research efforts aim to enhance the algorithms' resistance against advanced attacks, optimize their performance across diverse platforms, and develop standardized and secure hybrid cryptographic systems. The transition to post-quantum cryptography will involve challenges such as interoperability with legacy systems, the need for clear standards and regulatory guidance, and the costs associated with software and hardware updates. Continued engagement with the cryptographic community and monitoring of the evolving security landscape will be crucial for ensuring a secure and effective migration to post-quantum cryptography.
The article analyzes the current state and prospects of the standardization of post-quantum algorithms for asymmetric cryptographic transformations at the national and international levels. The main reasons for the transition to post-quantum cryptography are discussed, particularly the potential threats posed by quantum computers to existing cryptographic algorithms (RSA, ECC, etc.). An overview of the NIST competition for selecting standards for post-quantum key encapsulation mechanisms (KEM) and electronic signatures is provided, with detailed descriptions of the algorithms chosen for standardization (CRYSTALS-Kyber, CRYSTALS-Dilithium, FALCON, SPHINCS+, and HQC). Additionally, the article examines the role of ISO/IEC, ETSI, and IETF in developing international standards and recommendations. Special attention is given to Ukrainian national standards and initiatives, particularly the algorithms “Skelya” and “Vershyna,” their features, and their prospects for integration into international standards. The article emphasizes the importance and complexity of transitioning to quantum-resistant algorithms and outlines further steps for the successful implementation of post-quantum cryptography. Keywords: post-quantum cryptography, key encapsulation mechanisms, electronic signatures, standardization.
Abstract. In the digital age, cryptography is widely used in various important systems such as financial, military and government ones, medical records etc. The life of modern people is closely connected with the cryptography. We send messages via instant messengers without even considering in which way the security of communications and data is ensured. We buy things both online and transfer money with confidence in transaction security. The level of digitization of our society is constantly increasing, and the digital data needs a reliable protection, which makes cryptography a current topic. Cryptographic systems ensure our security and the basic properties of information, such as privacy, integrity, availability. However, with the beginning of the development of quantum computers, the field of cryptography has developed in a new direction. Quantum cryptography is a science that studies the methods of communication systems protection. It is based on the idea that patterns of quantum physics (physical properties described by the laws of quantum optics, quantum electrodynamics, or quantum field theory) are inviolable. The current state of development and usage of powerful quantum computers, as well as their mathematical and software, is strictly confidential and securely protected. Only clear-cut information about quantum computers and their usage in cryptography is provided. NIST has announced an open competition to select quantum-resistant public-key cryptographic algorithms. After the third round, CRYSTALS-KYBER, CRYSTALS Dilithium, FALCON, and SPHINCS+ were proposed to be standardized. NIST has already recommended moving from the sizes of keys and algorithms that provide 80 security bits to the sizes of keys and algorithms that provide 112 or 128 security bits in order to protect against classic attacks. Post-quantum cryptography, which with its complexities still requires a more detailed study, challenge science once more. However, it is unknown when the changes will occur and when the quantum era will begin, as well as what consequences they will have. It is only possible to predict how many advantages will have quantum calculations compared to usual, and how different the new quantum models will be from classic ones.
The paper considers post-quantum projects of the Falcon and Dilithium electronic signature standards (ES), which are finalists of the NIST USA competition. The mathematical apparatus of algebraic lattices and appropriate methods are used in their construction. In further study and comparison of these post-quantum ES draft standards, both from a theoretical and practical standpoint, it is fundamental to substantiate the requirements for parameters and keys and in general to calculate the main indicators according to the accepted conditional and unconditional criteria. In such studies, it is important to determine the sufficiency of ensuring the guarantee of their security against classical, quantum, special and error-based attacks. This can be ensured, inter alia, through a reasonable choice of the sizes of common parameters and keys, and their practical construction in accordance with the adopted security model. However, when choosing the sizes of common parameters and keys, a significant contradiction arises between the properties of the draft of the Falcon and Dilithium ES standards, So increasing the size of the general parameters and keys leads to an increase in the complexity of transformations, and vice versa. The purpose of this article consists in analysis of problematic issues of choosing the size of parameter and keys for post-quantum ES projects based on mathematical methods of Falcon and Dilithium, and features of their implementation, including implementation according to the adopted security model. Comparative analysis of the stability and complexity of the Falcon and Dilithium ES draft standards depending on the size of the parameters and keys, including for 6 and 7 security levels. Development of proposals for decisions on the adoption of national post-quantum ES standards based on the mathematical methods Falcon and Dilithium. Determining the influence of unconditional, conditional and pragmatic criteria on the advantages when deciding on the ES standardization based on Falcon and Dilithium mathematical methods, including taking into account the availability of patents and the need to obtain licenses, etc.
The 2024 NIST finalisation of post-quantum cryptography (PQC) standards -- CRYSTALS-Kyber (FIPS 203), CRYSTALS-Dilithium (FIPS 204), FALCON (FIPS 205), and SPHINCS+ -- marks the transition from research to deployment-ready quantum-resistant cryptography. This paper proposes the Post-Quantum Cryptography Algorithm Evaluation (PQCAE) framework, a systematic performance and security analysis of five NIST-standardised and candidate PQC algorithms across five deployment dimensions: key/signature size, computational performance, security level, implementation complexity, and hardware acceleration potential. PQCAE evaluates CRYSTALS-Kyber-768, CRYSTALS-Dilithium-3, FALCON-512, SPHINCS+-128s, and BIKE-L1 on three hardware platforms (x86-64 server, ARM Cortex-M4 embedded, and FPGA). CRYSTALS-Kyber achieves the best overall profile for key encapsulation -- fastest operations (KeyGen 0.06 ms, Encaps 0.08 ms, Decaps 0.09 ms on x86-64) with compact keys. FALCON-512 provides the smallest signature sizes (897 bytes) at moderate computational cost. SPHINCS+ offers the strongest conservative security (hash-based, no lattice assumptions) but largest signatures (8 KB). PQCAE provides migration guidance for organisations transitioning from classical to post-quantum cryptography.